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fThe Jordan-Brouwer Separation Theorem. The complement of the compact, connected hypersurface X in R consists of two connected open sets, the outside Do and the

\fThe Jordan-Brouwer Separation Theorem. The complement of the compact, connected hypersurface X in R" consists of two connected open sets, the "outside" Do and the "inside" D,. Moreover, D, is a compact manifold with boundary OD, = X

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